Minutes before kickoff, the pitch invader ran in front of the Hungary team with the rainbow flag.
The security personnel then brought him to the ground and he was applauded by the crowd.
This protest is taking place amid international condemnation of a Hungarian law banning the promotion or depiction of homosexuality to minors.
The Hungarian parliament passed the law on 16 June. It has been widely criticised, but the conservative government insists that the law is intended to protect children.
After UEFA turned down a request to light the Allianz Arena, Munich, in rainbow colours, rainbow flags were raised by fans at the Group F match.
The request by Munich mayor Dieterreiter was denied because it was political and was made in response to legislation that prohibited the promotion and display of homosexuality to minors in Hungary.
Reiter called UEFA's decision not to grant the request'shameful' and stated that other landmarks in the city would be displayed rainbow colours.
It is a symbol of our core values and promotes everything we believe in. We want a more just society that is open to all, regardless of background, beliefs, or gender.
"Some people have interpreted UEFA’s decision to decline the request of the city to light the Munich stadium with rainbow colors for a Euro 2020 match as 'political. The request was actually political and related to the presence of the Hungarian football team in the stadium for the match with Germany.
"The rainbow is not a symbol of political power for UEFA. It is a symbol of our firm commitment towards a more diverse, inclusive society."
Bayern Munich president Herbert Hainer stated Tuesday that he would like his club's stadium to glow in this manner for the match. He added: "Open-mindedness, tolerance and fair play are fundamental values that our society stands for."
Munich's town hall is decorated with rainbow flags. On Tuesday, the mayor of Munich stated that officials in the area planned to light the wind turbine next to the stadium and illuminate the Olympic tower in rainbow colors.
Reiter stated in a statement that "I find it shameful, that UEFA prohibits us to send a signal here in Munich for openness and tolerance, respect, and solidarity with the LGBTQI+ community."
"I'm also disappointed that the DFB (the German Football Association) despite its unbelievably clear position here in Munich, Bavaria, and also in Germany has not achieved or wished to achieve anything."
Ursula Von Der Leyen (president of the European Commission) has criticized the Hungarian bill. She said that it "goes against fundamental principles of European Union" and warned that the commission would use every power to protect rights of EU citizens.Updated Date: 23 June 2021, 16:50